shore regional high school district west long branch, …

SHORE REGIONAL HIGH SCHOOL DISTRICT

West Long Branch, New Jersey

Content Area: Mathematics

Course: Geometry

Mr. Leonard Schnappauf, Superintendent/Principal

Dr. Robert McGarry, Director of Curriculum and Instruction

BOARD OF EDUCATION

Anthony F. Moro, Jr., President Tadeusz “Ted” Szczurek, Vice President

Nancy DeScenza David Baker

Elizabeth Garrigal Diane Merla

Russell T. Olivadotti Ronald O’Neill

Frank J. Pingitore Paul Rolleri

Date of Last Revision and Board Adoption: 9/24/2009

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Mathematics

Geometry

REVISION PREPARED BY

Nicole Andreasi Jon Remedios

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Table of Contents

Mathematics Program Mission Statement…………………………...……………………………………………………………...….…4

Course Description and “Big Ideas”……………………………………………………….……………………….…………………..…4

Essential Questions ………………………………………………….………………………………………………………………….4-5

Primary (P) Content Area and Secondary (S) Areas of Focus…………………………………………………………………………….5

Benchmark Objectives………………………………………………………………………………………………………………….…5

Scope and Sequence……………………………………………………………………………………………………………………… 6

Learning Resources………………………………………………………………………………………………………………………..6

Grading Procedures………………………………………………….………………………………………………………………….6-7

Course Evaluation…………………………………………………………………………………………………………………………7

New Jersey Core Curriculum Content Standards/Cumulative Progress Indicators Addressed in the Course……………………..….8-23

Units of Study…………………………………………………………………………………………………………………….…..24-43

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Mathematics Program Mission Statement The mission of the Mathematics program at Shore Regional High School is to ensure that students develop an understanding of mathematical concepts and processes leading to individual mastery while logic and problem-solving skills assist students in becoming successful global citizens.

Course Description and “Big Ideas” In this course students will develop spatial sense through experiences that enable them to recognize, visualize, categorize, represent, and transform geometric shapes, and to apply their knowledge of geometric properties, relationships, and models to other areas of mathematics and to the physical world. Students will communicate mathematically using a variety of written, oral, symbolic, and visual forms of expression. Calculators, computers, models and geometric tools will be regularly used to enhance mathematical thinking, understanding, and power. Students will develop an understanding of measurement and systems of measurement to describe and analyze quantifiable phenomena. As with all courses in the mathematics program, this course introduces and/or reinforces the big ideas of number sense, geometry and measurement, patterns and algebra, and mathematical processes.

“Essential Questions”

Throughout this course and in the sequence of courses in this content area, students are consistently guided to consider the following essential questions:

1. Number Sense and Concepts a. When can estimation be used instead of exact measurements?

2. Geometry and Measurement a. How do we use properties of geometric shapes to solve problems in real world situations? b. How can the properties of geometric figures be verified using the coordinate plane? c. How do I apply problem-solving strategies to analyze real world situations involving measurements using different

units? d. How do area, perimeter, and surface area differ? How are they related dimensionally?

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e. How are properties of geometric figures related to their measurable attributes? f. How do I identify a variety of transformations in the real world and use them to help me understand geometric

properties? g. What is the Pythagorean Theorem and when is it useful? How are right triangles used to measure indirectly?

3. Patterns and Algebra a. How are geometric transformations represented as functional relationships?

4. Math Processes a. How do mathematicians use formal language to compare properties of geometric figures? b. How are similarity and congruence established? Why is this important? c. How do I recognize similarity in the real world and use ratios to create proportions that allow me to solve related

problems? The course also reinforces learning of other Standards and CPI’s already mastered and contributes to the development of mastery of other standards in the areas of [insert names of other secondary content areas].

Primary (P) Content Area and Secondary (S) Areas of Focus

Benchmark Objectives

These objectives focus on the achievement of the Standards/Big Ideas as they pertain to the specific course content and are listed in the units of study found within this document. Summative assessment of these objectives may occur at the point in the course when instruction of the components parts is completed (typically at the end of a unit), at the end of a marking period, end of the year, or in areas tested by the State when the tests are scheduled.

NJCCC Standard NJCCC Standard NJCCCS Standard 1. Visual and Performing Arts 5. Science 9. Career Education and Consumer/ Family/ Life Skills 2. Health and Physical Education 6. Social Studies 3. Language Arts Literacy 7. World Languages 4. Mathematics P 8. Technology Literacy

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Scope and Sequence This represents the order in which units or the “big ideas” of the course are taught. The specific unit content, CPI’s addressed, time frame for instruction and how proficiency will be addressed is included in the units that follow. This list serves the teacher as an overview of course implementation and administrators as a basis for review of lesson plans and orientation for classroom observation. The Units included in this course include:

1. Tools of Geometry 2. Perpendicular and Parallel Lines 3. Congruent Triangles 4. Relationships Within Triangles 5. Quadrilaterals 6. Similarity 7. Right Triangles and Trigonometry 8. Transformations 9. Surface Area and Volume 10. Circles

Learning Resources

(Textbooks, technology resourcess, media, primary documents, etc.).

1. Prentice Hall. Geometry. Textbook and resource materials. 2009 2. Muschla, Judith and Gary. Geometry Teacher’s Activities Kit. 2000 3. McDougal Littell resource materials. 2007 4. Teacher developed PowerPoint presentations

Grading Procedures The final course proficiency grade will be the average of the four marking period grades and the department prepared mid-year and final examinations aligned with NJCCCS/CPI and benchmarks for the content studied in the course.

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Marking period grades will be based on the average of unit grades and any special cross-unit projects. Unit assessments, delineated for each unit, will include such measures as:

1. Quizzes 2. Chapter tests

Course Evaluation

Course achievement will be evaluated as the percent of all pupils who achieve the minimum level of proficiency (final average grade) in the course. Student achievement levels above minimum proficiency will also be reported. Final grades, and where relevant mid-term and final exams, will be analyzed by staff for the total cohort and for sub-groups of students to determine course areas requiring greater support or modification). Course evaluation requires the pursuit of answers to the following questions:

1. To what extent is the course content, instruction and assessments aligned with the required NJCCS? 2. Are content, instruction and assessments sufficient to demonstrate student mastery of the Standards/CPI’s? 3. Do all students achieve the set proficiencies/benchmarks set for the course, including CPI’s designated to be reinforced,

introduced, and developed?

In this course, the goal is that a minimum of 95% of the pupil’s will meet at least the minimum proficiency level (D or better) set for the course. The department will analyze the achievement of students on Unit Assessments, Mid-term and Final Exams and Final Course Grades, with specific attention to the achievement of sub-groups identified by the state to determine if modifications in the curriculum and instructional methods are needed.

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New Jersey Core Curriculum Content Standards/Cumulative Progress Indicators Addressed in the Course Primary: Mathematics

4.1. Number and Numerical Operations

Cumulative Progress Indicator

A. Number Sense

Addressed in this

course?

1. Extend understanding of the number system to all real numbers

2. Compare and order rational and irrational numbers.

3. Develop conjectures and informal proofs of properties of number systems and sets of numbers. B. Numerical Operations

1. Extend understanding and use of operations to real numbers and algebraic procedures.

2. Develop, apply, and explain methods for solving problems involving rational and negative exponents.

3. Perform operations on matrices a. addition and subtraction b. scalar multiplication

4. Understand and apply the laws of exponents to simplify expressions involving numbers raised to powers.

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C. Estimation

1. Recognize the limitations of estimation, assess the amount of error resulting from estimation, and determine whether the error is within acceptable tolerance limits.

4.2 (Geometry and measurement) All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.

Cumulative Progress Indicator A. Geometric Properties

Addressed in this course?

1. Use geometric models to represent real-world situations and objects and to solve problems using those models (e.g., use Pythagorean Theorem to decide whether an object can fit through a doorway).

1. Draw perspective views of 3D objects on isometric dot paper, given 2D representations (e.g., nets

or projective views).

2. Apply the properties of geometric shapes.

• Parallel lines – transversal, alternate interior angles, corresponding angles • Triangles

a. Conditions for congruence b. Segment joining midpoints of two sides is parallel to and half the length of the third

side

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c. Triangle Inequality d. Special right triangles

• Minimal conditions for a shape to be a special quadrilateral • Circles – arcs, central and inscribed angles, chords, tangents • Self-similarity • Counterexamples to incorrect conjectures

4. Use reasoning and some form of proof to verify or refute conjectures and theorems.

Verification or refutation of proposed proofs Simple proofs involving congruent triangles Counterexamples to incorrect conjectures

B. Transforming Shapes

Addressed in this

course? • Determine, describe, and draw the effect of a transformation, or a sequence of

transformations, on a geometric or algebraic representation, and, conversely, determine whether and how one representation can be transformed to another by a transformation or a sequence of transformations.

1. Recognize three-dimensional figures obtained through transformations of two-dimensional figures (e.g., cone as rotating an isosceles triangle about an altitude), using software as an aid to visualization.

3. Determine whether two or more given shapes can be used to generate a tessellation

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4. Generate and analyze iterative geometric patterns.

Fractals (e.g., Sierpinski’s Triangle) Patterns in areas and perimeters of self-similar figures Outcome of extending iterative process indefinitely

C. Coordinate Geometry Addressed in this

course?

1. Use coordinate geometry to represent and verify properties of lines and line segments. Distance between two points Midpoint and slope of a line segment Finding the intersection of two lines Lines with the same slope are parallel Lines that are perpendicular have slopes whose product is –1

2. Show position and represent motion in the coordinate plane using vectors. Addition and subtraction of vectors

D. Units of Measurement

Addressed in this

course? • Understand and use the concept of significant digits.

1. Choose appropriate tools and techniques to achieve the specified degree of precision and error needed in a

situation. Degree of accuracy of a given measurement tool Finding the interval in which a computed measure (e.g., area or volume) lies, given the degree of

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precision of linear measurements

E. Measuring Geometric Objects

Addressed in this

course?

• Use techniques of indirect measurement to represent and solve problems.

Similar triangles Pythagorean theorem Right triangle trigonometry (sine, cosine, tangent)

1. Use a variety of strategies to determine perimeter and area of plane figures and surface area and volume of

3D figures.

Approximation of area using grids of different sizes Finding which shape has minimal (or maximal) area, perimeter, volume, or surface area under given

conditions using graphing calculators, dynamic geometric software, and/or spreadsheets Estimation of area, perimeter, volume, and surface area

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4.3 (Patterns and algebra) All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.

Cumulative Progress Indicator

A. Patterns

Addressed in this

course?

1. Use models and algebraic formulas to represent and analyze sequences and series.

Explicit formulas for nth terms Sums of finite arithmetic series Sums of finite and infinite geometric series

2. Develop an informal notion of limit.

3. Use inductive reasoning to form generalizations.

B. Functions and Relationships


1. Understand relations and functions and select, convert flexibly among, and use various representations for them, including equations or inequalities, tables, and graphs.

2. Analyze and explain the general properties and behavior of functions or relations, using algebraic and

graphing techniques.

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Slope of a line Domain and range Intercepts Continuity Maximum/minimum Estimating roots of equations Solutions of systems of equations Solutions of systems of linear inequalities using graphing techniques Rates of change

3. Understand and perform transformations on commonly-used functions.

Translations, reflections, dilations Effects on linear and quadratic graphs of parameter changes in equations Using graphing calculators or computers for more complex functions

4. Understand and compare the properties of classes of functions, including exponential, polynomial,

rational, and trigonometric functions.

Linear vs. non-linear Symmetry Increasing/decreasing on an interval

C. Modeling


1. Use functions to model real-world phenomena and solve problems that involve varying quantities.

Linear, quadratic, exponential, periodic (sine and cosine), and step functions (e.g., price of

mailing a first-class letter over the past 200 years)

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Direct and inverse variation Absolute value Expressions, equations and inequalities Same function can model variety of phenomena Growth/decay and change in the natural world Applications in mathematics, biology, and economics (including compound interest)

2. Analyze and describe how a change in an independent variable leads to change in a dependent one.

3. Convert recursive formulas to linear or exponential functions (e.g., Tower of Hanoi and doubling).

D. Procedures Addressed in this course?

• Evaluate and simplify expressions.

Add and subtract polynomials Multiply a polynomial by a monomial or binomial Divide a polynomial by a monomial Perform simple operations with rational expressions Evaluate polynomial and rational expressions

2. Select and use appropriate methods to solve equations and inequalities.

Linear equations and inequalities – algebraically Quadratic equations – factoring (including trinomials when the coefficient of x2 is 1) and using the

quadratic formula Literal equations All types of equations and inequalities using graphing, computer, and graphing calculator techniques

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2. Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those

carried out by technology.

4.4 (Data analysis, probability, and discrete mathematics) All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.

Cumulative Progress Indicator A. Data Analysis (or Statistics)

Addressed in this

course?

1. Use surveys and sampling techniques to generate data and draw conclusions about large groups. Advantages/disadvantages of sample selection methods (e.g., convenience sampling, responses to

survey, random sampling)

2. Evaluate the use of data in real-world contexts.

Accuracy and reasonableness of conclusions drawn Correlation vs. causation Bias in conclusions drawn (e.g., influence of how data is displayed) Statistical claims based on sampling

3. Design a statistical experiment, conduct the experiment, and interpret and communicate the outcome.

4. Estimate or determine lines of best fit (or curves of best fit if appropriate) with technology, and use

them to interpolate within the range of the data.

5. Analyze data using technology, and use statistical terminology to describe conclusions.

Measures of dispersion: variance, standard deviation, outliers Correlation coefficient Normal distribution (e.g., approximately 95% of the sample lies between two standard deviations

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on either side of the mean)

6. Distinguish between randomized experiments and observational studies.

B. Probability

1. Calculate the expected value of a probability-based game, given the probabilities and payoffs of the

various outcomes, and determine whether the game is fair.

• Use concepts and formulas of area to calculate geometric probabilities.

2. Model situations involving probability with simulations (using spinners, dice, calculators and computers)

and theoretical models, and solve problems using these models.

3. Determine probabilities in complex situations.

Conditional events Complementary events Dependent and independent events

4. Estimate probabilities and make predictions based on experimental and theoretical probabilities.

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5. Understand and use the “law of large numbers” (that experimental results tend to approach theoretical

probabilities after a large number of trials).

C. Discrete Mathematics—Systematic Listing and Counting

1. Calculate combinations with replacement (e.g., the number of possible ways of tossing a coin 5 times and

getting 3 heads) and without replacement (e.g., number of possible delegations of 3 out of 23 students).

2. Apply the multiplication rule of counting in complex situations, recognize the difference between

situations with replacement and without replacement, and recognize the difference between ordered and unordered counting situations.

3. Justify solutions to counting problems.

4. Recognize and explain relationships involving combinations and Pascal’s Triangle, and apply those

methods to situations involving probability.

D. Discrete Mathematics—Vertex-Edge Graphs and Algorithms

1. Use vertex-edge graphs and algorithmic thinking to represent and solve practical problems.

Circuits that include every edge in a graph Circuits that include every vertex in a graph

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Scheduling problems (e.g., when project meetings should be scheduled to avoid conflicts) using graph coloring

Applications to science (e.g., who-eats-whom graphs, genetic trees, molecular structures)

2. Explore strategies for making fair decisions.

Combining individual preferences into a group decision (e.g., determining winner of an election or

selection process) Determining how many Student Council representatives each class (9th, 10th, 11th, and 12th grade) gets

when the classes have unequal sizes (apportionment)

4.5 (Mathematical processes) All students will use mathematical processes of problem solving, communication, connections, reasoning, representations, and technology to solve problems and communicate mathematical ideas.

Cumulative Progress Indicator A. Problem Solving

Addressed in this

course? 1. Learn mathematics through problem solving, inquiry, and discovery.

2. Solve problems that arise in mathematics and in other contexts (cf. workplace readiness standard 8.3).

Open-ended problems Non-routine problems Problems with multiple solutions Problems that can be solved in several ways

3. Select and apply a variety of appropriate problem-solving strategies (e.g., "try a simpler problem" or "make a diagram") to solve problems.

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4. Pose problems of various types and levels of difficulty.

5. Monitor their progress and reflect on the process of their problem solving activity.

B. Communication Addressed in this

course? 1. Use communication to organize and clarify their mathematical thinking.

Reading and writing Discussion, listening, and questioning

2. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others, both orally and in writing.

3. Analyze and evaluate the mathematical thinking and strategies of others.

4. Use the language of mathematics to express mathematical ideas precisely.

C. Connections Addressed in this

course? 1. Recognize recurring themes across mathematical domains (e.g., patterns in number, algebra, and

geometry).

2. Use connections among mathematical ideas to explain concepts (e.g., two linear equations have a unique solution because the lines they represent intersect at a single point).

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3. Recognize that mathematics is used in a variety of contexts outside of mathematics.

4. Apply mathematics in practical situations and in other disciplines.

5. Trace the development of mathematical concepts over time and across cultures (cf. world languages and social studies standards).Use the language of mathematics to express mathematical ideas precisely.

6. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

D. Reasoning Addressed in this

course? 1. Recognize that mathematical facts, procedures, and claims must be justified.

2. Use reasoning to support their mathematical conclusions and problem solutions.

3. Select and use various types of reasoning and methods of proof.

4. Rely on reasoning, rather than answer keys, teachers, or peers, to check the correctness of their problem solutions.

5. Make and investigate mathematical conjectures.

Counterexamples as a means of disproving conjectures

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Verifying conjectures using informal reasoning or proofs.

6. Evaluate examples of mathematical reasoning and determine whether they are valid.

E. Representations Addressed in this

course? 1. Create and use representations to organize, record, and communicate mathematical ideas.

Concrete representations (e.g., base-ten blocks or algebra tiles) Pictorial representations (e.g., diagrams, charts, or tables) Symbolic representations (e.g., a formula) Graphical representations (e.g., a line graph)

2. Select, apply, and translate among mathematical representations to solve problems.

3. Use representations to model and interpret physical, social, and mathematical phenomena.

F. Technology Addressed in this

course? 1. Use technology to gather, analyze, and communicate mathematical information.

2. Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information (cf. workplace readiness standard 8.4-D).

3. Use graphing calculators and computer software to investigate properties of functions and their

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graphs.

4. Use calculators as problem-solving tools (e.g., to explore patterns, to validate solutions).

5. Use computer software to make and verify conjectures about geometric objects.

6. Use computer-based laboratory technology for mathematical applications in the sciences (cf. science standards).

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Unit 1: Tools of Geometry

Unit Question(s) Objectives Resources Formative Assessment Strategies

Pacing Guide

Marking Period

1. How do we use properties of geometric shapes to solve problems in real world situations?

2. When can estimation be used instead of exact measurements?

3. How can the properties of geometric figures be verified using the coordinate plane?

4. How do I apply problem-solving strategies to analyze real world situations involving measurements using different units?

5. How do area, perimeter, and surface area differ? How are they related dimensionally?

Students will be able to:

1. Define and describe patterns

2. Understand and use basic undefined and defined terms of Geometry.

3. Use segment postulates and distance formula.

4. Classify angles.

5. Bisect segments and angles.

6. Identify vertical and linear pairs.

7. Identify complementary and supplementary angles.

8. Find perimeter and area.

1. Prentice Hall. Geometry. Textbook and resource materials. 2009

2. Muschla, Judith and Gary. Geometry Teacher’s Activities Kit. 2000

3. McDougal Littell resource materials. 2007

4. Teacher developed PowerPoint presentations

1. Homework

2. Quizzes 3. Classwork

4. Mini whiteboards

15 days 1

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Standards

Instructional Activities, Methods, and Assignments

Unit Summative Assessment(s)

4.1.A.1, 4.1.A.3, 4.1.B.1, 4.2.A.1, 4.2.A.2, 4.2.A.3, 4.2.B.2, 4.2.C.1, 4.2.E.2, 4.3.A.1, 4.3.A.3, 4.3.D.1, 4.3.D.2, 4.5.A.1, 4.5.A.2, 4.5.A.3, 4.5.A.4, 4.5.A.5, 4.5.B.1, 4.5.B.2, 4.5.B.3, 4.5.B.4, 4.5.C.1, 4.5.D.1, 4.5.D.2, 4.5.D.3, 4.5.D.4, 4.5.D.5, 4.5.D.6, 4.5.E.1, 4.5.E.2, 4.5.E.3, 4.5.F.1, 4.5.F.2, 4.5.F.4, 4.5.F.5

1. Survivor Game

2. Bingo

3. Chapter Practices (A, B, or C), pending on level of students

4. Crossword Puzzle of the Language of Geometry

5. A Geometry “Word” Puzzle

1. Chapter Test

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Unit 2: Perpendicular and Parallel Lines

Unit Question(s) Objectives Resources Formative

Assessment Strategies

Pacing Guide

Marking Period


2. When can estimation be used instead of exact measurements?



5. How do mathematicians use formal language to compare properties of geometric figures?


1. Identify relationships between lines

2. Identify angles formed by transversals

3. Prove and use results about parallel lines and transversals

4. Use the properties of parallel lines to solve real world problems

5. Prove that two lines are parallel 6. Construct parallel lines using

straightedge and compass 7. Find slopes of lines and use

slopes to identify parallel and perpendicular lines

8. Write equations of parallel and perpendicular lines in the plane.





1. Homework 2. Quizzes

3. Classwork 4. Mini

whiteboards

15 days 1

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Standards



4.1.B.l, 4.2.A.l, 4.2.A.3, 4.2.A.4, 4.2.C.1, 4.3.A.1, 4.3.A.3, 4.3.B.1, 4.3.B.2, 4.3.C.1, 4.3.C.2, 4.3.D.2, 4.5.A.1, 4.5.A.3, 4.5.C.2,

4.5.D.5, 4.5.E.1

1. Survivor Game

2. Bingo


4. Angle Pairs Investigation

5. Drawing Intersections Investigations

6. Monopoly and Perpendicular and Parallel Lines

1. Chapter Test

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Unit 3: Congruent Triangles


Pacing Guide

Marking Period



3. How are properties of geometric figures related to their measurable attributes?

4. How are similarity and congruence established? Why is this important?


1. Classify triangles by their sides and angles.

2. Find angle measures in triangles. 3. Identify congruent figures and

corresponding parts. 4. Prove that two triangles are congruent

using SSS, SAS, ASA, AAS, HL. 5. Use congruence postulates and

theorems in real life problems. 6. Use properties of Isosceles,

Equilateral, and Right Triangles.





1. Homework

2. Quizzes

3. Classwork

4. Mini whiteboards

18 days 1-2

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Standards



4.1.B.1, 4.2.A.1, 4.2.A.3, 4.2.A.4, 4.3.D.2, 4.5.D.5,

1. Survivor Game

2. Bingo


4. The Big Triangle Problem

5. Identifying What is Needed to Prove Triangles are Congruent Investigation

1. Chapter Test

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Unit 4: Relationships Within Triangles


Pacing Guide

Marking Period

1. How do we use properties of geometric shapes to solve problems in real world situations? 2. How do mathematicians use formal language to compare properties of geometric figures? 3. How are properties of geometric figures related to their measurable attributes?

4. How are similarity and congruence established? Why is this important?


1. Use properties of Perpendicular Bisectors

2. Use properties of Angle Bisectors 3. Identify bisectors, medians, and

altitudes 4. Identify the midsegments of a triangle 5. Use properties of midsegments 6. Use triangle measurements to

determine largest angle or side 7. Use Triangle Inequality





1. Homework

2. Quizzes

3. Classwork

4. Mini whiteboards

10 days 2

31

Standards



4.1.A.2, 4.1.B.1, 4.2.A.1, 4.2.A.3, 4.2.A.4, 4.3.A.3, 4.3.D.2, 4.3.D.3, 4.5.A.3, 4.5.C.3, 4.5.D.1, 4.5.D.2, 4.5.D.3, 4.5.D.5, 4.5.D.6

1. Survivor Game

2. Bingo


4. Drawing Medians of Triangles

5. Attributes of Triangles Table

6. Triangles: The Points, Segments, and Angles Activity

1. Chapter Test

32

Unit 5: Quadrilaterals


Pacing Guide

Marking Period







1. Identify polygons 2. Use the sum of the measures of the

interior angles or quadrilaterals 3. Use properties of parallelograms in

real life situations 4. Prove quadrilaterals are

parallelograms 5. Use coordinate geometry with

parallelograms 6. Use properties of special

quadrilaterals 7. Identify special quadrilaterals based

on limited information 8. Find the areas of triangles and

quadrilaterals





1. Homework

2. Quizzes

3. Classwork

4. Mini whiteboards

24 days 2

33

Standards



4.1.A.1, 4.1.B.1, 4.1.B.4, 4.2.A.1, 4.2.A.3, 4.2.A.4, 4.2.B.1, 4.2.C.1, 4.2.D.1, 4.2.D.2, 4.2.E.1, 4.2.E.2, 4.3.A.3, 4.3.B.3, 4.3.C.2, 4.3.D.2, 4.3.D.3, 4.4.B.2, 4.4.B.3, 4.4.B.4, 4.4.B.5, 4.4.B.6, 4.5.A.2, 4.5.C.2,

4.5.D.3, 4.5.E.1

1. Survivor Game

2. Bingo


4. Attributes of Quadrilaterals Table

5. Classifying Quadrilaterals Table

6. The Big Quadrilateral Puzzle

1. Chapter Test

34

Unit 6: Similarity


Pacing Guide

Marking Period







7. How do I recognize similarity in the real world and use ratios to create proportions that allow me to solve related problems?

8. How are geometric transformations represented as functional relationships?


1. Find and simplify the ratio of two numbers

2. Use properties of proportions 3. Use proportions to solve real

world problems 4. Identify similar polygons 5. Use similar polygons to solve

real world problems 6. Use similarity theorems to

prove that two triangles are similar

7. Use proportionality theorems to calculate segment length

8. Use proportionality theorems to solve real world problems

1. PPrentice Hall. Geometry. Textbook and resource materials. 2009

2. MMuschla, Judith and Gary. Geometry Teacher’s Activities Kit. 2000

3. MMcDougal Littell resource materials. 2007

4. TTeacher developed PowerPoint presentations

1. Homework

2. Quizzes

3. Classwork

4. Mini whiteboards

15 days 3

35

Standards



4.1.A.1, 4.1.B.1, 4.2.A.1, 4.2.A.3, 4.2.A.4, 4.2.D.1, 4.2.D.2, 4.2.E.1, 4.3.D.1, 4.3.D.2, 4.5.C.1, 4.5.C.4

1. Survivor Game

2. Bingo 3. Chapter Practices (A, B, or C), pending on level of students

4. Proving Triangles Similar Activity and Practice

1. Chapter Test

36

Unit 7: Right Triangles and Trigonometry


Pacing Guide

Marking Period





5. What is the Pythagorean Theorem and when is it useful? How are right triangles used to measure indirectly?


1. Simplify, add, subtract, multiply, divide, and rationalize radicals

2. Use Pythagorean Theorem and its converse to solve real life problems

3. Use side lengths to classify triangles by their angle measures

4. Find the side lengths of special right triangles

5. Use Special Right Triangles to solve real life problems

6. Find the sine, cosine, and tangent of an acute angle

7. Use trig ratios to solve real world problems

8. Solve a right triangle 9. Find the magnitude and direction of

a vector 10. Add, subtract, and scalar multiply

vectors





1. Homework

2. Quizzes

3. Classwork

4. Mini whiteboards

16 days 3

37

Standards



4.1.A.1, 4.1.B.1, 4.1.B.4, 4.2.A.1, 4.2.A.4, 4.2.C.1, 4.2.C.2, 4.2.D.1, 4.2.D.2, 4.2.E.1, 4.3.D.2, 4.3.D.3, 4.5.B.2, 4.5.B.3, 4.5.C.5,

1. Survivor Game

2. Bingo


4. Proving the Pythagorean Theorem

5. Explaining the Sine, Cosine, and Tangent Ratios Activity

6. Right Triangles and Special Right Triangles Activity

1. Chapter Test

38

Unit 8: Transformations


Pacing Guide

Marking Period



3. How do I identify a variety of transformations in the real world and use them to help me understand geometric properties?



1. Identify the 3 basic rigid transformations

2. Use transformation in real life situations

3. Identify relationships between reflections and line of symmetry

4. Use vectors in real life situations 5. Identify glide reflections in a plane 6. Represent transformation as

composition of simpler transformations





1. Homework

2. Quizzes

3. Classwork

4. Mini whiteboards

15 days 3

39

Standards



4.1.B.1, 4.1.B.3, 4.2.A.1, 4.2.B.1, 4.2.B.3, 4.2.B.4,

4.3.D.3

1. Survivor Game

2. Bingo


4. Drawing Transformations Activity

5. The Basics of Transformations Worksheet

6. Writing Directions for Transformaions Activity

1. Chapter Test

40

Unit 9: Surface Area and Volume


Pacing Guide

Marking Period







1. Find the volume of a given solid 2. Find the surface area of a given

solid 3. Compare the surface area and

volumes of similar solids





1. Homework

2. Quizzes

3. Classwork

4. Mini whiteboards

16 days 4

41

Standards



4.1.A.1, 4.1.B.1, 4.1.B.4, 4.2.A.2, 4.2.B.2, 4.2.D.1, 4.1.D.2, 4.2.E.1, 4.2.E.2, 4.3.A.3, 4.3.D.2, 4.3.D.3, 4.5.A.1, 4.5.A.3, 4.5.E.3

1. Survivor Game

2. Bingo


4. Volume, Surface Area, and Candy!

5. Types of Solids Chart

6. Solids by Numbers

1. Chapter Test

42

Unit 10: Circles


Pacing Guide

Marking Period







1. Identify segments and lines related to circles

2. Use properties of a tangent to a circle

3. Use properties of arcs of circles and of chords of circles

4. Use inscribed angles to solve problems

5. Use properties of inscribed polygons

6. Use angles formed by tangents and chords to solve problems in Geometry

7. Use angles formed by lines that intersect a circle to solve problems

8. Find the lengths of segments of chords, tangents, and secants

9. Write the equation of a circle 10. Use the equation of a circle and its

graph to solve problems





1. Homework

2. Quizzes

3. Classwork

4. Mini whiteboards

14 days 4

43

Standards



4.1.B.4, 4.2.A.2, 4.2.A.3, 4.2.A.4, 4.2.C.1, 4.2.C.2, 4.2.D.1, 4.2.D.2, 4.2.E.1, 4.3.B.1, 4.3.D.1, 4.3.D.2,

4.3.D.3, 4.5.B.1

1. Survivor Game

2. Bingo


4. A Crossword Puzzle of Circle Vocabulary

5. The Big Circle Puzzle

6. Explain the Reason: Circles

7. Circles: Symbols of Segments and Angles-

1. Chapter Test

shore regional high school district west long branch, …

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